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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='color:black'>Hi Richard<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Thank you.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Here you go:<o:p></o:p></span></p><p class=MsoNormal><img width=494 height=377 id="Picture_x0020_1" src="cid:image001.png@01D0865D.EBF61D40"><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><img width=431 height=389 id="Picture_x0020_2" src="cid:image002.png@01D0865E.019EDA60"><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org] <b>On Behalf Of </b>Richard Gauthier<br><b>Sent:</b> Monday, May 04, 2015 10:43 AM<br><b>To:</b> Nature of Light and Particles - General Discussion<br><b>Subject:</b> Re: [General] Electron Torus<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Hi Chip,<o:p></o:p></p><div><p class=MsoNormal> Both tori should be symmetrical above and below the z-axis and center on z=0.<o:p></o:p></p></div><div><p class=MsoNormal> Richard<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p><div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><p class=MsoNormal>On May 4, 2015, at 8:16 AM, Chip Akins <<a href="mailto:chipakins@gmail.com">chipakins@gmail.com</a>> wrote:<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>Hi Richard<o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal><image001.jpg><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal>Viewed from the Z axis:<o:p></o:p></p></div><div><p class=MsoNormal><image002.jpg><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal>And from the equatorial plane:<o:p></o:p></p></div><div><p class=MsoNormal><image003.jpg><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal>Chip<o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><div><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span class=apple-converted-space><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span></span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>General [<a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org"><span style='color:#954F72'>mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</span></a>]<span class=apple-converted-space> </span><b>On Behalf Of<span class=apple-converted-space> </span></b>Richard Gauthier<br><b>Sent:</b><span class=apple-converted-space> </span>Sunday, May 03, 2015 11:07 PM<br><b>To:</b><span class=apple-converted-space> </span>Nature of Light and Particles - General Discussion<br><b>Subject:</b><span class=apple-converted-space> </span>Re: [General] position</span><o:p></o:p></p></div></div></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><div><p class=MsoNormal>Chip and all,<o:p></o:p></p></div></div><div><div><p class=MsoNormal> Here are some equations that relate to the modeling of a circulating photon as an electron. The second and third set include my own model of the photon. The first set doesn’t require a particular model for the photon, except as mentioned below. The first model is the one that generates the de Broglie wavelength as explained in my article mentioned below.<o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal>1. Here is the set of parametric equations for the helical trajectory of double-looping photon that models a free electron, and whose circular radius for a resting electron is Ro=hbar/2mc. The speed of the photon along this trajectory is always c. The longitudinal or z-component of the photon’s speed is the electron’s velocity v along the z-axis. The frequency of the photon around the helical axis is proportional to the circulating photon/electron's energy E=gamma mc^2. The distance of the photon’s helical trajectory from the z-axis for an electron whose speed is v, is proportional to 1/gamma^2. This equation is in my article “The electron is a charged photon with the de Broglie wavelength”. This equation does not include a particular model of the photon, but assumes that the photon follows the relations c=f lambda, E=hf and p=h/lambda. Both helicities of the helical trajectory are given.<o:p></o:p></p></div></div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Helvetica",sans-serif'>_______________________________________________<br>If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at<span class=apple-converted-space> </span></span><a href="mailto:richgauthier@gmail.com"><span style='font-size:9.0pt;font-family:"Helvetica",sans-serif;color:#954F72'>richgauthier@gmail.com</span></a><span style='font-size:9.0pt;font-family:"Helvetica",sans-serif'><br><a href="</span><a href="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/richgauthier%40gmail.com?unsub=1&unsubconfirm=1"><span style='font-size:9.0pt;font-family:"Helvetica",sans-serif;color:#954F72'>http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/richgauthier%40gmail.com?unsub=1&unsubconfirm=1</span></a><span style='font-size:9.0pt;font-family:"Helvetica",sans-serif'>"><br>Click here to unsubscribe<br></a></span><o:p></o:p></p></div></blockquote></div><p class=MsoNormal><o:p> </o:p></p></div></div></body></html>